Recent Comments
Giving a talk at Eli… on Academic Degrees and Sex Johan Aspegren on To Cheer You Up in Difficult T… To cheer you up in d… on Another sensation – Anni… Gil Kalai on To Cheer You Up in Difficult T… Gil Kalai on To Cheer You Up in Difficult T… Alexander Barvinok on To Cheer You Up in Difficult T… Kevin on To Cheer You Up in Difficult T… Gil Kalai on To Cheer You Up in Difficult T… Arseniy on To Cheer You Up in Difficult T… Alexander Barvinok on To Cheer You Up in Difficult T… uniform on To Cheer You Up in Difficult T… Arseniy on To Cheer You Up in Difficult T…
Tag Archives: Convex polytopes
Karim Adiprasito: Flag simplicial complexes and the non-revisiting path conjecture (A combinatorial proof of the Adiprasito-Benedetti theorem.)
This post is authored by Karim Adiprasito The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction. Jesus de Loera and Steve Klee described simplicial polytopes which are not … Continue reading
Posted in Convex polytopes, Guest blogger
Tagged Convex polytopes, Flag complexes, Hirsch conjecture, Karim Adiprasito
Leave a comment
Tokyo, Kyoto, and Nagoya
Near Nagoya: Firework festival; Kyoto: with Gunter Ziegler; with Takayuki Hibi, Hibi, Marge Bayer, Curtis Green and Richard Stanly; Tokyo: Peter Frankl; crowded crossing. Added later: Mazi and I at the same restaurant taken by Stanley. I just returned from … Continue reading
Posted in Combinatorics, Conferences, Convex polytopes
Tagged Alternating sign matrices, Convex polytopes, FPSAC, Japan
2 Comments
Projections to the TSP Polytope
Michael Ben Or told me about the following great paper Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds by Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary and Ronald de Wolf. The paper solves an old conjecture … Continue reading
Test Your Intuition (12): Perturbing a Polytope
Let P be a d-dimensional convex polytope. Can we always perturb the vertices of P moving them to points with rational coordinates without changing the combinatorial structure of P? In order words, you require that a set of vertices whose … Continue reading
Posted in Convex polytopes, Test your intuition
Tagged Convex polytopes, Test your intuition
4 Comments
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the just-posted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The d-step Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments
Igor Pak’s “Lectures on Discrete and Polyhedral Geometry”
Here is a link to Igor Pak’s book on Discrete and Polyhedral Geometry (free download) . And here is just the table of contents. It is a wonderful book, full of gems, contains original look on many important directions, things that … Continue reading
Posted in Book review, Convex polytopes, Convexity
Tagged Convex polytopes, Convexity, Igor Pak, rigidity
4 Comments
Five Open Problems Regarding Convex Polytopes
The problems 1. The conjecture A centrally symmetric d-polytope has at least non empty faces. 2. The cube-simplex conjecture For every k there is f(k) so that every d-polytope with has a k-dimensional face which is either a simplex … Continue reading
